Block \(\mathbf {LU}\) factors of generalized companion matrix pencils

DOI10.1016/j.tcs.2007.04.019zbMath1140.65032OpenAlexW2008774323MaRDI QIDQ995569

D. A. Aruliah, Amirhossein Amiraslani, Robert M. Corless

Publication date: 3 September 2007

Published in: Theoretical Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.tcs.2007.04.019

zbMATH Keywords

matrix polynomialsblock LU factoringblock pivoting strategiescompanion matrix pencilspolynomial eigenvalues

Mathematics Subject Classification ID

Related Items (5)

The formulae and algorithms for Lagrange-power basis transformation and Lagrange-Newton transformation ⋮ The equivalence of the constrained Rayleigh quotient and Newton methods for matrix polynomials expressed in different polynomial bases along with the confluent case ⋮ Block \(\mathbf {LU}\) factors of generalized companion matrix pencils ⋮ Parallel Krylov Solvers for the Polynomial Eigenvalue Problem in SLEPc ⋮ Notes on linear factor polynomial deflation in polynomial bases

Uses Software

• Matlab
• mctoolbox
• OPQ

Cites Work

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• Bernstein-Bézoutian matrices
• Linear construction of companion matrices
• A generalized Rayleigh quotient iteration for lambda-matrices
• Block \(\mathbf {LU}\) factors of generalized companion matrix pencils
• A companion matrix resultant for Bernstein polynomials
• Linearization of matrix polynomials expressed in polynomial bases
• Solving Polynomials with Small Leading Coefficients
• Barycentric Lagrange Interpolation
• The numerical stability of barycentric Lagrange interpolation
• Accuracy and Stability of Numerical Algorithms
• A resultant matrix for scaled Bernstein polynomials

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